Measurement of branching fraction ratios for B+ → D*+D−K+, B+ → D*−D+K+, and B0 → D*−D0K+ decays

Abstract

A measurement of four branching-fraction ratios for three-body decays of B mesons involving two open-charm hadrons in the final state is presented. Run 1 and Run 2 pp collision data are used, recorded by the LHCb experiment at centre-of-mass energies 7, 8, and 13 TeV and corresponding to an integrated luminosity of 9 fb−1. The measured branching-fraction ratios areBB+→D∗+D−K+BB+→D¯0D0K+=0.517±0.015±0.013±0.011,BB+→D∗−D+K+BB+→D¯0D0K+=0.577±0.016±0.013±0.013,BB0→D∗−D0K+BB0→D−D0K+=1.754±0.028±0.016±0.035,BB+→D∗+D−K+BB+→D∗−D+K+=0.907±0.033±0.014,$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast +}{D}^{-}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {\overline{D}}^0{D}^0{K}^{+}\right)}=0.517\pm 0.015\pm 0.013\pm 0.011,\ {}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast -}{D}^{+}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {\overline{D}}^0{D}^0{K}^{+}\right)}=0.577\pm 0.016\pm 0.013\pm 0.013,\ {}\begin{array}{c}\frac{\mathcal{B}\left({B}^0\to {D}^{\ast -}{D}^0{K}^{+}\right)}{\mathcal{B}\left({B}^0\to {D}^{-}{D}^0{K}^{+}\right)}=1.754\pm 0.028\pm 0.016\pm 0.035,\ {}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast +}{D}^{-}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {D}^{\ast -}{D}^{+}{K}^{+}\right)}=0.907\pm 0.033\pm 0.014,\end{array}\end{array}} $$where the first of the uncertainties is statistical, the second systematic, and the third is due to the uncertainties on the D-meson branching fractions. These are the most accurate measurements of these ratios to date.